Multivariable And Parametric Functions

Description

Suppose we wanted to turn the multivariable function,

(1)
\begin{equation} f(x, y) = (x^4 - 5x^2 + 4 + y^2)^2 \end{equation}

into a parametric function, where

(2)
\begin{equation} x = f(t) = 2t + 5 \end{equation}

and

(3)
\begin{equation} y = g(t) = 3t - 1 \end{equation}

We can use Sage to accomplish this.

Sage Cell

Code

var('y t')
f(x, y) = (x^4 - 5*x^2 + 4 + y^2)^2
f(x=2*t+5, y=3*t-1)

Options

Expanding the output

The above cell produces a correct, but not easily readable output. We can clean it up with .expand()

Code

var('y t')
f(x, y) = (x^4 - 5*x^2 + 4 + y^2)^2
f(x=2*t+5, y=3*t-1).expand()

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Date: 04 Mar 2019 16:24

Submitted by: Zane Corbiere

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